Problem: $\dfrac{d}{dx}\left(x^{^{\scriptsize\dfrac{2}{3}}}\right)=$
The derivative can be found using the power rule : $\dfrac{d}{dx}(x^n)=n\cdot x^{n-1}$ (Remember that this applies even when $n$ is a fraction.) $\begin{aligned} &\phantom{=}\dfrac{d}{dx}\left(x^{^{\frac{2}{3}}}\right) \\\\ &=\dfrac{2}{3}x^{^{\frac{2}{3}-1}} \gray{\text{The power rule}} \\\\ &=\dfrac{2}{3}x^{^{-\frac{1}{3}}} \end{aligned}$ In conclusion, we found that $\dfrac{d}{dx}\left(x^{^{\frac{2}{3}}}\right)=\dfrac{2}{3}x^{^{-\frac{1}{3}}}$. This can also be written as $\dfrac{2}{3\sqrt[3]x}$ (all equivalent forms are accepted).